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Opossum: Difference between revisions

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See [[Porcupine family #Opossum]] for technical data.
See [[Porcupine family #Opossum]] for technical data.


== Tuning spectrum ==
== Interval chain ==
In the following table, odd harmonics 1–11 and their inverses are in '''bold'''.
 
{| class="wikitable center-1 right-2"
|-
! #
! Cents*
! Approximate ratios*
|-
| 0
| 0.0
| '''1/1'''
|-
| 1
| 160.0
| 10/9, 11/10, 12/11, 15/14
|-
| 2
| 320.0
| 6/5, 11/9
|-
| 3
| 480.0
| '''4/3''', 9/7
|-
| 4
| 640.0
| 10/7, '''16/11''', 22/15
|-
| 5
| 800.0
| '''8/5''', 11/7
|-
| 6
| 960.0
| 12/7, '''16/9'''
|-
| 7
| 1120.0
| 40/21, 48/25, 64/33
|-
| 8
| 80.0
| 16/15, 36/35
|-
| 9
| 240.0
| '''8/7'''
|}
<nowiki/>* In 15edo tuning, octave reduced
 
== Tunings ==
{| class="wikitable center-1 mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Least-squares tunings
|-
! Target
! Generator
! Eigenmonzo
|-
| 5-odd-limit
| ~10/9 = 162.996{{c}}
| 262144/234375
|-
| 7-odd-limit
| ~10/9 = 158.732{{c}}
| {{Monzo| 0 -5 3 19 }}
|-
| 9-odd-limit
| ~12/11 = 159.481{{c}}
| {{Monzo| 0 3 2 22 }}
|-
| 11-odd-limit
| ~12/11 = 159.564{{c}}
| {{Monzo| -27 2 1 9 -1 }}
|-
| 13-odd-limit
| ~12/11 = 158.421{{c}}
| {{Monzo| 0 15 6 34 -1 -15 }}
|-
| 15-odd-limit
| ~12/11 = 159.377{{c}}
| {{Monzo| 0 32 23 35 -5 -21 }}
|}
 
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>generator
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Generator (¢)
! Comments
! Comments
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|  
|  
| 150.000
| 150.000
|  
| 8d val, lower bound of 7-odd-limit diamond monotone
|-
|-
|  
|  
| 12/11
| 11/6
| 150.637
| 150.637
|  
|  
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|-
|-
|  
|  
| 14/13
| 13/7
| 153.100
| 153.100
|  
|  
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|-
|-
|  
|  
| 14/11
| 11/7
| 156.498
| 156.498
|  
|  
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|  
|  
| 156.522
| 156.522
|  
| 23bcf val
|-
|-
|  
|  
| 6/5
| 5/3
| 157.821
| 157.821
|  
|  
|-
|
| {{vector|0 15 6 34 -1 -15}}
| 158.421
| 13 limit least squares
|-
|-
| 5\38
| 5\38
|  
|  
| 157.895
| 157.895
|  
| 38bceff val
|-
|-
| 7\53
| 7\53
|  
|  
| 158.491
| 158.491
|  
| 53bcefff val
|-
|-
|  
|  
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|-
|-
|  
|  
| {{vector|0 -5 3 19}}
| 7/4
| 158.732
| 7 limit least squares
|-
|
| 8/7
| 159.019
| 159.019
| 7, 9, 11, 13 and 15 limit minimax
| 7-, 9-, 11-, 13- and 15-odd-limit minimax
|-
|-
|  
|  
| 18/13
| 13/9
| 159.154
| 159.154
|  
|  
|-
|
| {{vector|0 32 23 35 -5 -21}}
| 159.377
| 15 limit least squares
|-
|
| {{vector|0 3 2 22}}
| 159.481
| 9 limit least squares
|-
|
| 1815912315/1476395008
| 159.564
| 11 limit least squares
|-
|-
| 2\15
| 2\15
|  
|  
| 160.000
| 160.000
|  
| Upper bound of 7-odd-limit diamond monotone<br>9- and 11-odd-limit diamond monotone (singleton)
|-
|-
|  
|  
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| 5/4
| 5/4
| 162.737
| 162.737
| 5 limit minimax
| 5-odd-limit minimax
|-
|
| 262144/234375
| 162.996
| 5 limit least squares
|-
|-
|  
|  
| 16/15
| 15/8
| 163.966
| 163.966
|  
|  
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|-
|-
|  
|  
| 4/3
| 3/2
| 166.015
| 166.015
|  
|  
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|-
|-
|  
|  
| 16/13
| 13/8
| 179.736
| 179.736
|  
|  
|-
|-
|  
|  
| 10/9
| 9/5
| 182.404
| 182.404
|  
|  
|}
|}


[[Category:Temperaments]]
[[Category:Opossum| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Exotemperaments]]
[[Category:Porcupine family]]
[[Category:Porcupine family]]
[[Category:Trienstonic clan]]
[[Category:Trienstonic clan]]
[[Category:Starling temperaments]]
[[Category:Starling temperaments]]
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